# What is the maximum value that the graph of z=10-12w-2w^2?

Nov 26, 2016

maximum value: $\textcolor{g r e e n}{28}$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} z = 10 - 12 w - 2 {w}^{2}$

The vertex will occur at the point where
$\textcolor{w h i t e}{\text{XXX}} \frac{\mathrm{dz}}{\mathrm{dw}} = 0$
and since the coefficient of ${w}^{2}$ is negative, the vertex sill be a maximum

In this case $\frac{\mathrm{dz}}{\mathrm{dw}} = - 12 - 4 w$
so the maximum will occur when $w = - 3$
and $z = 10 - 12 \cdot \left(- 3\right) - 2 \cdot {\left(- 3\right)}^{2}$
$\textcolor{w h i t e}{\text{XXX}} = 10 + 36 - 18$
$\textcolor{w h i t e}{\text{XXX}} = 28$